Finite Group DatabasebetaFinite Group Databasebeta| order | 34596 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×#16838652⋊C3 |
| unambiguous semidirect product | #16838652⋊C32 |
| unambiguous semidirect product | (C3×#16838652)⋊C3 |
| Fitting, socle | C3×C312 ⋊ C3×C4 |
| derived, Sylow | C312 ⋊ C32×C4 |
| Hall | C3×#15668332 ⋊ C4 |
| Hall | #16838652 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #16838652⋊C3 |
| commutator, hypocenter | C312 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C312 | C3×C4 |
| prime radical | C3×#19153443 | C2 |
| cosocle | C31⋊D31 | C2×C32 |
| LCS | G ▷ C312 | |
| UCS | C1 ◁ C3 | |
228 conjugacy classes of subgroups.
| transitive degree | μt(G) = 186 |
276 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34596, 141);